login
A259565
a(1) = 1, for n > 1 a(n) = smallest number not already in the sequence such that the arithmetic mean of two neighboring terms is a squarefree number.
6
1, 3, 7, 5, 9, 11, 15, 13, 17, 21, 23, 19, 25, 27, 31, 29, 33, 35, 39, 37, 41, 43, 49, 45, 47, 55, 51, 59, 57, 53, 61, 63, 67, 65, 69, 71, 75, 73, 81, 77, 79, 85, 87, 83, 89, 93, 95, 91, 97, 105, 99, 103, 101, 109, 111, 107, 113, 115, 121, 117, 119, 125, 129
OFFSET
1,2
COMMENTS
A259605(n) = (a(n) + a(n+1)) / 2;
conjecture: sequence is a permutation of the odd numbers;
a(A259570(n)) = 2*n-1.
LINKS
PROG
(Haskell)
import Data.List (delete)
a259565 n = a259565_list !! (n-1)
a259565_list = 1 : f 1 [3, 5 ..] where
f x zs = g zs where
g (y:ys) = if a008966 ((x + y) `div` 2) == 1
then y : f y (delete y zs) else g ys
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jun 30 2015
STATUS
approved